Kramers theory in the relaxation dynamics of a tilted asymmetric periodic potential

Takaaki Monnai, Ayumu Sugita, Katsuhiro Nakamura

Research output: Contribution to journalArticle

5 Citations (Scopus)


We investigate the low-temperature relaxation dynamics toward a nonequilibrium steady state in a tilted asymmetric periodic potential based on the WKB analysis and the numerical diagonalization of the Fokker-Planck operator. Due to the tilting, the Fokker-Planck operator, and thus the Schrödinger operator associated with it, are non-Hermitian. Therefore, we evaluate the decay rate based on the WKB analysis both for real- and complex-valued eigenvalues. In the tilting range where the double-humped barrier exists, the decay rate is shown to obey a law which is a subtle nonequilibrium extension of the so-called Kramers escape rate. The decay rate for the single-humped barrier case is analyzed as well. The large tilting regime where the barriers no longer exist is also investigated.

Original languageEnglish
Article number031140
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number3
Publication statusPublished - 2007 Sep 28


ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this